Since there's been no detail from RP about where the RN allegedly blew it so badly, it's interesting to look at what reality (rather than the view with hindsight but no insight) seems to look like. The basic problem is that the German heavy ships can cruise at 26 knots (30 mph) and the British heavy ships cruise at 20 knots (23 mph) because of the lower speed of Valiant and Nelson.
From the German base at Wilhelmshaven to the Stavanger region, the closest point of Norway to Scapa, is 400 miles or 13.3 hours steaming for the Germans. The distance from Scapa to Stavanger is about 286 miles or 12.4 hours steaming for the RN. So one major problem for the RN becomes apparent - the Germans can get steam up and by the time they leave the Jade the British have just 50 minutes to spot them, send and process the sighting report, get orders out, and leave Scapa or else they cannot catch the Germans. That isn't possible - apart from the fact that the Germans dislike British recce sitting around off their major port, ships need at least an hour to get up steam and then they have to raise anchor, leave the harbour and work up to speed.
In addition, the RN must obviously be concerned about the possibility of heavy ships breaking out into the Atlantic. Their concern was very well founded since Lutzow had been meant to break out during Weserebung, and that plan was thwarted only by the finding of a mechanical issue. So when there was news that a German fleet was at sea, the Home Fleet headed NNE which is the best course to stop a German breakout, but takes them away from the closest point to Norway.
Once the Germans have passed Stavanger the geometry changes against the British even more. The Germans will be beyond the closest point to Scapa, and heading further away from Scapa as the coast heads NNE. The British will be in a stern chase - and they are slower. So how on earth were the British supposed to catch the German heavy ships?
The chart that CT put up indicates that the British recce patrols reached about 45 miles from the Danish coast. Hhaar says that the German forces bound for the two northern destinations were sighted by a Hudson at about 8:48 am when off Esbjerg in Denmark with about 112 statute miles covered since leaving the Jade. They were bombed that day by a dozen Blenheims with no damage. Visibility was less than a mile by the afternoon of 7 April.
The sighting report didn't reach Forbes, the commander of the Home Fleet, until 11.20am. And the report only mentioned one cruiser (probably a light one) and some destroyers - not heavy ships. The Hudson had been chased off by fighter cover so understandably could not get in close to get a perfect idea of the composition of the fleet. But even as we have seen, if the Hudson's report was transmitted straight to Forbes and he decided to send the whole fleet out after what was reported as a cruiser and some destroyers, he still did not have enough time to intercept the German heavy ships.
The slower German groups heading to the south and leaving later could have been caught by the British, but on the morning of April 8 again visibility closed in to less than a mile and they could not be spotted.
Yes the British did have one carrier (Furious) which was undergoing some work at the time of the invasion but got her Swordfish back on board quickly and went to sea after the British battleships had left. Even if she had been with the battleships her search pattern would very likely to have been aimed at finding ships aiming to break out into the Atlantic and therefore unlikely to find ships hugging the coast as the German ones were. I don't know where Renown was at the time but it is possible that Forbes may have been able to split Renown, Repulse and Furious into a fast group but given that is putting two old battlecruisers (one unmodernised) up against two new battlecruisers it is the sort of splitting forces that could have led to disaster, and left the most powerful ships (Nelson and Valiant) without a carrier and therefore without a ship that can slow down the faster Germans to allow them to be brought to battle.
Once it was realised that the Germans were invading Norway there is a chance, perhaps, that they would have been in reach of Furious' Swordfish but I haven't done the sums, and the weather was often terrible - the German destroyers lost no less than 10 men overboard in one night shortly after leaving port due to gales. Early war carrier strikes were often unsuccessful especially in the north and in that sort of weather.
Given these realities it does not seem reasonable to claim that the RN "shat in its hand" in failing to intercept the German ships.
